I'm not sure if this is right but here goes......You said you want a smaller pillow & wanted to "reduce" the long side. The fabric is 19 inches x 15 inches.
Keeping the same ratio, if reducing/cutting the fabric:
19-15=4 19-4=15. Add 1/2 inch seams to each side = fabric would be 16 inches long
15-4=11. Add 1/2 inch seams to each side = 12 inches wide.
So you would cut the fabric 16 inches long x 12 inches wide. After sewing the pillow would be 15 inches long x 11 inches wide.
Now if you are only reducing one side, since you stated you wanted it reduced in length. Then all you do is turn it around so you have 15 inches long x 19 wide, instead of 19 inches long x 15 inches wide. No cutting.